This is evidently the core of Cloudflare's business strategy, emerging in practically everything they do tactically; from Matthew Prince having an epic public sook earlier this year about AWS's network team telling him to jump in a lake, to this. Peering drives down the marginal cost of bandwidth, and this is super relevant since Cloudflare's main value-add product is DDoS mitigation. Unless you're an incumbent tier 1 carrier (which is the hereditary royalty of networking), the classic ways to obtain more/better peering are either have the most eyeballs, or the most content. A typical access ISP takes the former approach, a CDN like Cloudflare takes the latter.
As usual, free anything means you are the commodity being traded on.
The fact of it is evident from the Cloudflare blog, but I don't particularly recommend giving that the time of day, since as with all content marketing it is also self-serving humbug.
Similarly they can use slow storage for most files and use their existing caching solutions for storing frequently accessed files.
They'll probably lose some money on customers who use lots of bandwidth, and make lots of money on everyone else.
Funny thing, paying for egress bandwidth is not something you do if you handle your own peering and other internet infrastructure. Paying for bandwidth is something that the cloud providers came up with to add further margin. So they likely pay $0/TB for that bandwidth.